Yes, you could use the term lexical order here. Usually, if one has a well-ordered list of orders $P_\alpha$, then one may define the lexical order on the product of the underlying space by placing $\vec x$ before $\vec y$ if the first difference $x_\alpha$ is before $y_\alpha$ in $P_\alpha$. In your case, you don't have orders, but merely pre-orders (since two sheep could have the same age, etc.). 

But also, you have the same underlying set in each case (the set of sheep), and so you don't want to look at the product space, but only at individual sheep, placing $x$ before $y$ if the least $\alpha$ where they are not equivalent has $x$ before $y$ in $P_\alpha$.